Show:
If-Then Form
Counter-
Example
Converse
Contrapositive
Inverse
100
Tenth graders are in Geometry.
"If you are a tenth grader, then you are in Geometry."
100
If x squared = 9, then x = -3.
"If x squared = 9, then x = 3"
100
If a child is 5 years old, then they are in kindergarden.
"If a child is in kindergarden, then they are 5 years old"
100
If you like tennis, then you play on the tennis team.
"If you do not play on the tennis team, then you do not like tennis"
100
If x is odd, then 3x is odd.
"If x is not odd, then 3x is not odd"
200
Puppies are small.
"If it is a puppy, then it is small"
200
All flags have green parts on them.
The American flag does not have green on it.
200
If there is snow on the ground, flowers are not in bloom.
"If flowers are not in bloom, then there is snow on the ground."
200
If x is odd, then 2x is even.
"If 2x is not even, then x is not odd."
200
If you like hockey, then you will go to the hockey game.
"If you do not like hockey, then you will not go to the hockey game."
300
A line contains at least 2 points.
"If it is a line, then it contains at least 2 points."
300
If the area of a swimming pool is 60 square meters, then its sides are 10 meters and 6 meters.
Its sides could be 12 meters and 5 meters.
300
If 2 lines intersect, then they cross each other.
"If 2 lines cross each other, then they intersect."
300
If a point lies on 2 lines, then it is at the intersection.
"If a point is not at the intersection, then it does not lie on 2 lines."
300
If you visited the White House, then you've been to Washington D.C.
"If you have not visited the White House, then you have not been to Washington D.C."
400
2x is larger than x when x is positive.
"If x is positive, then 2x is larger than x." OR "If 2x is larger than x, then x is positive."
400
A polygon can have only two right angles.
A square has four right angles.
400
If it is snowing, then it is cold. Is the converse of this statement true or false, and why?
"If it is cold, then it is snowing." FALSE - it can be cold without snowing
400
If you like purple, then you love Barney.
"If you do not love Barney, then you do not like purple."
400
If you are 16, then you can legally drive. Is the inverse of this statement true or false, and why?
"If you are not 16, then you can not legally drive." FALSE - those older than 16 can also legally drive
500
An if-then statement has two parts, known as the ___ and the ___
The hypothesis and the conclusion
500
All prime numbers are odd.
2 is a prime number.
500
What is the mathematical notation for the converse? (Hint: The regular conditional is notated p --> q)
q --> p
500
What is the mathematical notation for the contrapositive? (Hint: A regular conditional is noted p --> q)
~q --> ~p
500
What is the mathematical notation for inverse? (Hint: The regular conditional is notated p --> q)
~p --> ~q